Engineering Statics

F-25


Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.

A vertical cut will be used for dA.  The value of y for the given curve is substituted for y.
The expression for the moment of inertia about the y axis is given.
Since dA = y dx and the value of y has been found, the integral can be 
set up as a function of x only.  The limits along the x axis go from 
0 to a.
Constants are factored out of the integral and variables are multiplied.
The integral is separated into two integrals.
The integration is performed.

The terms are simplified.
Further simplification:
The value for the moment of inertia about the y axis is found.